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oai:drops-oai.dagstuhl.de:11872 2024-03-06T10:48:53Z ddc:004 open_access

An FPT Algorithm for Minimum Additive Spanner Problem Kobayashi, Yusuke Graph algorithms Fixed-parameter tractability Graph spanner For a positive integer t and a graph G, an additive t-spanner of G is a spanning subgraph in which the distance between every pair of vertices is at most the original distance plus t. The Minimum Additive t-Spanner Problem is to find an additive t-spanner with the minimum number of edges in a given graph, which is known to be NP-hard. Since we need to care about global properties of graphs when we deal with additive t-spanners, the Minimum Additive t-Spanner Problem is hard to handle and hence only few results are known for it. In this paper, we study the Minimum Additive t-Spanner Problem from the viewpoint of parameterized complexity. We formulate a parameterized version of the problem in which the number of removed edges is regarded as a parameter, and give a fixed-parameter algorithm for it. We also extend our result to the case with both a multiplicative approximation factor α and an additive approximation parameter β, which we call (α, β)-spanners. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Yusuke Kobayashi 2020 Is Part Of LIPIcs, Volume 154, 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2020.11 urn:nbn:de:0030-drops-118729 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2020.11 eng https://creativecommons.org/licenses/by/3.0/legalcode